# How do you solve 4-p/(p-1)=2/(p-1)?

Jan 17, 2017

$p = 2$

#### Explanation:

$4 - \frac{p}{p - 1} = \frac{2}{p - 1}$ is equivalent to

$4 = \frac{p}{p - 1} + \frac{2}{p - 1}$

or $4 = \frac{p + 2}{p - 1}$

or $4 \times \textcolor{red}{\left(p - 1\right)} = \frac{p + 2}{p - 1} \times \textcolor{red}{\left(p - 1\right)}$

or $4 p - 4 = p + 2$

or $4 p \textcolor{red}{- p} - 4 \textcolor{red}{+ 4} = p \textcolor{red}{- p} + 2 \textcolor{red}{+ 4}$

or $3 p = 6$

or $3 p \times \frac{1}{3} = 6 \times \frac{1}{3} = \frac{6}{3} = 2$

i.e. $p = 2$